Introduction: The l1 minimization technique has been empirically demonstrated to exactly recover an S-sparse signal with about 3S-5S measurements [1]. In order to get exact reconstruction with smaller number of measurements, recently, for static images, Trzasko [2] has proposed homotopic l0 minimization technique. Instead of minimizing the l0 norm which achieves best possible theoretical bound ...

Tensors are increasingly common in several areas such as data mining, computer graphics, and computer vision. Tensor clustering is a fundamental tool for data analysis and pattern discovery. However, there usually exist outlying data points in realworld datasets, which will reduce the performance of clustering. This motivates us to develop a tensor clustering algorithm that is robust to the out...

A bounded linear operator between Banach spaces is called completely continuous if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for the class of non-completely-continuous operators from L1 into an arbitrary Banach space, namely, the operator from L1 into l∞ defined by

Recently, many l1-norm based PCA methods have been developed for dimensionality reduction, but they do not explicitly consider the reconstruction error. Moreover, they do not take into account the relationship between reconstruction error and variance of projected data. This reduces the robustness of algorithms. To handle this problem, a novel formulation for PCA, namely angle PCA, is proposed....

We address the problem of a succinct static data structure representing points on anM M grid (M = 2m where m is size of a word) that permits to answer the question of finding the closest point to a query point under the L1 or L1 norm in constant time. Our data structure takes essentially minimum space. These results are extended to d dimensions underL1 .